code: def _correlation_matrix_using_hypersphere_decomposition(
      num_assets, thetas, dtype=None
  ):
      """Rebonato-Jaeckel method to generate valid correlation matrix.
  
      The method returns a valid correlation matrix using the hypersphere
      decomposition approach described in Ref [1].
  
      #### References:
      [1]: Riccardo Rebonato, Peter Jaeckel, The Most General Methodology to Create
           a Valid Correlation Matrix for Risk Management and Option Pricing
           Purposes.
      https://papers.ssrn.com/sol3/Delivery.cfm/SSRN_ID1969689_code1760921.pdf?abstractid=1969689&mirid=1
  
      Args:
        num_assets: An integer `Tensor` specifying the number of correlated assets.
        thetas: A real `Tensor` of shape `[num_assets * (num_assets - 1)]`
          specifying the angles used for the construction of the correlation matrix.
        dtype: The default dtype to use when converting values to `Tensor`s.
          Default value: `None` which means that default dtypes inferred by
            TensorFlow are used.
  
      Returns:
        A real `Tensor` of shape `(num_assets, num_assets)` containing the
        correlation matrix derived from `thetas` using the hypersphere
        decomposition method.
      """
      thetas = tf.convert_to_tensor(thetas, dtype=dtype)
      dtype = dtype or thetas.dtype
      thetas = tf.reshape(thetas, shape=[num_assets, num_assets - 1])
      cos_theta = tf.math.cos(thetas)
      cos_theta = tf.concat(
          [cos_theta, tf.ones([num_assets, 1], dtype=dtype)], axis=1
      )
      sin_cumprod = tf.math.cumprod(tf.math.sin(thetas), axis=-1)
      sin_cumprod = tf.concat(
          [tf.ones([num_assets, 1], dtype=dtype), sin_cumprod], axis=1
      )
      j = tf.expand_dims(tf.range(1, num_assets + 1), axis=0)
      corr_matrix = tf.where(
          j < num_assets, cos_theta * sin_cumprod, sin_cumprod
      )
      corr_matrix = tf.linalg.matmul(
          corr_matrix, corr_matrix, transpose_b=True
      )
  
      return corr_matrix
  
file_path: tf-quant-finance/tf_quant_finance/models/hjm/calibration.py
imports: from typing import Callable, Tuple
  import numpy
  import tensorflow.compat.v2
  import tensorflow_probability
  from tf_quant_finance import types
  from tf_quant_finance import utils
  from tf_quant_finance.black_scholes import implied_vol
  from tf_quant_finance.black_scholes.implied_vol_utils import UnderlyingDistribution
  from tf_quant_finance.math import make_val_and_grad_fn
  from tf_quant_finance.math import optimizer
  from tf_quant_finance.math import random
  from tf_quant_finance.models import valuation_method
  from tf_quant_finance.models.hjm.swaption_pricing import price
  from tf_quant_finance.rates.analytics import swap
label_desc: Use image node_id 1 for calling a global function with example usage: _correlation_matrix_using_hypersphere_decomposition(num_assets, thetas, dtype) and returns: corr_matrix